PROBLEM LINK:

Practice
Contest

Author:Konstantin Sokol
Tester:Gerald Agapov
Editorialist:Tasnim Imran Sunny

DIFFICULTY:

Simple

PREREQUISITES:

Ad-Hoc, Map

PROBLEM:

Given a string S which is consisted of characters ‘A’, ‘B’ or 'C'. Find the number of substrings of S which have equal number of ‘A’s, ‘B’s and ‘C’s.

EXPLANATION:

Let,
A_i = Number of ‘A’s in S between the indexes 1 and i (inclusive).
B_i = Number of ‘B’s in S between the indexes 1 and i (inclusive).
C_i = Number of ‘C’s in S between the indexes 1 and i (inclusive).

Let’s consider the substring S_j...i :
Number of ‘A’-s in that substring = A_i - A_j-1
Number of ‘B’-s in that substring = B_i - B_j-1
Number of ‘C’-s in that substring = C_i - C_j-1

So for that substring to be good: A_i - A_j-1 = B_i - B_j-1 = C_i - C_j-1

Alternatively the following two conditions are enough for that substring to be good:

A_i - B_i = A_j-1 - B_j-1
A_i - C_i = A_j-1 - C_j-1

Go from left to right and for each index i find the number of valid good substrings which ends at i. The number of such substrings would be the number of indexes k (k < i) where (A_i - B_i, A_i - C_i )= (A_k - B_k, A_k - C_k ). That can be obtained if the pair (A_k - B_k, A_k - C_k )for all k are stored in a key-value storage where the key being the pair and value being the number indexes having that difference pair. If using C++, STL Map can be used. The author did not use a map, instead he computed all the difference pairs and then sorted those and then find the number of equal pairs.

AUTHOR'S AND TESTER'S SOLUTIONS:

Author's solution can be found here.
Tester's solution can be found here.